Optimal Control Jumping Algorithm

A jump is an easy way to test the controls needed to make the robot dog take a step, as it captures the rapid change in dynamics between supporting the weight of the dog and being free in the air.
This jump was simulated in Gazebo Sim with a lower level cartesian impedance controller running at 1khz and a LTV-MPC optimal controller running at 100hz

First Try: Motor packaging 

The initial design for the leg focused on minimizing inertia by using carbon fiber and placing the motors as close to the pivot as possible. This approach faced a significant packaging challenge, as the selected ODrive motors are much bulkier than those used in traditional designs. Our first attempt to solve this involved moving the knee motor in front of the leg, but this solution proved suboptimal because it created significant "stickout" and failed to fully remove the motor's mass from the leg's inertia.

Improvement: Coaxial Drive

The second design iteration, a coaxial drive, solves the "stickout" and inertia problems from the previous version. This was achieved by mounting the knee motor directly on top of the hip motor. In this configuration, power is transferred to the knee joint through a sprocket that is coaxial with the hip's axis of rotation. This design allows the knee motor to remain stationary relative to the robot's body, which effectively removes its significant mass from the leg's moment of inertia and makes the leg even more agile.